Explanation of the cw operation of theEr3+3-μm crystal laser

Abstract

A computer simulation of the ${\mathrm{Er}}^{3+}$ 3-μm crystal laser considering the full rate-equation scheme up to the ${}_{}{}^4{}_{}{}^{}$ ${\mathit{F}}_{7/2}$ level has been performed. The influence of the important system parameters on lasing and the interaction of these parameters has been clarified with multiple-parameter variations. Stimulated emission is fed mainly by up-conversion from the lower laser level and in many cases is reduced by the quenching of the lifetime of this level. However, also without up-conversion a set of parameters can be found that allows lasing. Up-conversion from the upper laser level is detrimental to stimulated emission but may be compensated by cross relaxation from the ${}_{}{}^4{}_{}{}^{}$ ${\mathit{S}}_{3/2}$ level. For a typical experimental situation we started with the parameters of ${\mathrm{Er}}^{3+}$:${\mathrm{LiYF}}_4$. In addition, the host materials ${\mathrm{Y}}_3$ ${\mathrm{Al}}_5$ ${\mathrm{O}}_{12}$ (YAG), ${\mathrm{YAlO}}_3$, ${\mathrm{Y}}_3$ ${\mathrm{Sc}}_2$ ${\mathrm{Al}}_3$ ${\mathrm{O}}_{12}$ (YSGG), and ${\mathrm{BaY}}_2$ ${\mathrm{F}}_8$, as well as the possibilities of codoping, are discussed. In view of the consideration of all excited levels up to ${}_{}{}^4{}_{}{}^{}$ ${\mathit{F}}_{7/2}$, all lifetimes and branching ratios, ground-state depletion, excited-state absorption, three up-conversion processes as well as their inverse processes, stimulated emission, and a realistic resonator design, this is, to our knowledge, the most detailed investigation of the ${\mathrm{Er}}^{3+}$ 3-μm crystal laser performed so far.